Solve (x^6-x^5+x^4-x^3+{x}^2-x-1+3/x+1)*(x+1)=

$$( { x }^{ 6 } - { x }^{ 5 } + { x }^{ 4 } - { x }^{ 3 } + { x }^{ 2 } -x-1+ \frac{ 3 }{ x+1 } ) \times (x+1)=$$

Evaluate

$$x^{7}-2x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1 times \frac{x+1}{x+1}.

$$\left(\frac{\left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)}{x+1}+\frac{3}{x+1}\right)\left(x+1\right)$$

Since \frac{\left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)}{x+1} and \frac{3}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)+3}{x+1}\left(x+1\right)$$

Do the multiplications in \left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)+3.

$$\frac{x^{7}+x^{6}-x^{6}-x^{5}+x^{5}+x^{4}-x^{4}-x^{3}+x^{3}+x^{2}-x^{2}-x-x-1+3}{x+1}\left(x+1\right)$$

Combine like terms in x^{7}+x^{6}-x^{6}-x^{5}+x^{5}+x^{4}-x^{4}-x^{3}+x^{3}+x^{2}-x^{2}-x-x-1+3.

$$\frac{x^{7}-2x+2}{x+1}\left(x+1\right)$$

Cancel out x+1 and x+1.

$$x^{7}-2x+2$$

Expand

$$x^{7}-2x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1 times \frac{x+1}{x+1}.

$$\left(\frac{\left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)}{x+1}+\frac{3}{x+1}\right)\left(x+1\right)$$

Since \frac{\left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)}{x+1} and \frac{3}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)+3}{x+1}\left(x+1\right)$$

Do the multiplications in \left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x-1\right)\left(x+1\right)+3.

$$\frac{x^{7}+x^{6}-x^{6}-x^{5}+x^{5}+x^{4}-x^{4}-x^{3}+x^{3}+x^{2}-x^{2}-x-x-1+3}{x+1}\left(x+1\right)$$

Combine like terms in x^{7}+x^{6}-x^{6}-x^{5}+x^{5}+x^{4}-x^{4}-x^{3}+x^{3}+x^{2}-x^{2}-x-x-1+3.

$$\frac{x^{7}-2x+2}{x+1}\left(x+1\right)$$

Cancel out x+1 and x+1.

$$x^{7}-2x+2$$